Asymptotic behaviour of Verblunsky coefficients

[摘要] Let V(z) = Pi(m)(j=1)(z - xi(j)), xi(h) not equal xi(k), h not equal k and vertical bar xi(j)vertical bar = m, and consider the polynomials orthogonal with respect to vertical bar V vertical bar(2) d mu, psi(n)(vertical bar V vertical bar(2) d mu; z), where mu is a finite positive Borel measure on the unit circle with infinite points in its support, such that the reciprocal of its Szego function has an analytic extension beyond vertical bar z vertical bar < 1. In this paper we deduce the asymptotic behaviour of their Verblunsky coefficients. By means of this result, an asymptotic representation for these polynomials inside the unit circle is also obtained. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] orthogonal polynomials;Verblunsky coefficients